This figure illustrates the discriminability differences between the different encoding rules considered in this study. Each dot represents the discriminability value for a pair of numerosity values and presented on a given trial to the participants in Experiment 1. For the sampling models, the discriminability rule is defined as
where corresponds to the respective Accuracy maximizing (A), Reward maximizing (R) or Decision by Sampling (D) encoding rules. For the logarithmic model (L) the discriminability rule is defined as
The color of each dot represents the log of the number of occurrences for the pairs of input values and . Note that the encoding values of the presented numerosities are different depending on the encoding rule, which makes it possible to identify the participants’ encoding strategy. Also note that for our imposed prior distribution, the DbS encoding rule is similar to the logarithmic rule, which explains the smaller difference in the quantitative predictions between these two models. Nevertheless, DbS was always the model that provided the best quantitative and qualitative predictions irrespective of incentivized goals.